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Lectures On K theory
This book covers the following topics: Topological K-Theory, Topological Preliminaries on Vector Bundles, Homotopy, Bott Periodicity and Cohomological Properties, Chern Character and Chern Classes, Analytic K-Theory, Applications of Adams operations, Higher Algebraic K-Theory, Algebraic Preliminaries and the the Grothendieck Group, The Whitehead and the Steinberg Groups.
Author(s): Ioannis P. ZOIS
137 Pages 
This book contains below topics, Direct Sums, Inner Products, Tensor Product s, Associated Fiber Bundles, Clutching Functions, The Universal Bundle, Cell Structures on Grassmannians, Paracompac tness, The Fundamental Product Theorem, Deducing Periodicity from the Product T heorem, Extending to a Cohomology Theory.
Author(s): Allen Hatcher
124 Pages
This paper considers smooth extensions of cohomology theories. It constructs a multiplicative model of smooth K theory, and a push forward for a proper submersion with a smooth K orientation. It also lifts the Chern character to this smooth setting.
Author(s): Ulrich Bunke, Thomas Schick
93 Pages
Algebraic K theory of real topological K theory
This book contains below topics, Hochschild homology and motivic filtrations, Filtering the motivic associated graded, Detection, Prismatic cohomology, Syntomic cohomology, Topological cyclic homology and algebraic Ktheory.
Author(s): Gabriel Angelini-Knoll, Christian Ausoni, John Rognes
59 Pages
On the integral algebraic K theory of Morava K theory
This note contains below topics, On the TC of formal DGAs with polynomial homology, The May filtration on topological negative cyclic homology and topological periodic cyclic homology, Cardinality of topological cyclic homology, Coefficients in algebraically closed fields, On the algebraic Ktheory of truncated witt vectors, On the algebraic Ktheory of motivic pullback squares, Bockstein spectral sequences and syntomic cohomology, On the K 1 local algebraic Ktheory of K 1.
Author(s): Gabriel Angelini-Knoll, Haldun Özgür Bay?nd?r
58 Pages
This book contains below topics, Prerequisites, General properties of the Kgroup of a TPC, Filtered chain complexes, Barcodes step functions and Ktheory for persistence modules, A Ktheoretic pairing, Measurements on the Kgroup and on barcodes, Symplectic Applications.
Author(s): Paul Biran, Octav Cornea, Jun Zhang
68 Pages
Lecture Notes for Algebraic and Hermitian K Theory
This note covers the following topics, Recollections and preliminaries, Symmetric monoidal and stable categories, The group completion theorem and the K theory of finite fields, The K theory of stable categories.
Author(s): Fabian Hebestreit, University of Bonn
257 Pages
Lecture Notes On The K theory Of Operator Algebras
This lecture note covers the following topics,Projections and Unitaries, The K0Group for Unital C Algebras, K1Functor and the Index Map, Bott Periodicity and the Exact Sequence of KTheory, Tools for the computation of Kgroups.
Author(s): Rainer Matthes and Wojciech Szymansk
92 Pages
Introduction To K theory and Some Applications
This book explains the following topics, Topological Ktheory, Ktheory of C algebras, Geometric and Topological Invarients, THE FUNCTORS K1 K2, K1, SK1 of Orders and Grouprings, Higher Algebraic Ktheory, Higher Dimensional Class Groups of Orders and Group rings, Higher Ktheory of Schemes, Modm Higher Ktheory of exact Categories, Schemes and Orders, Profinite Higher Ktheory of Exact Categories, Schemes and Orders, Equivariant Higher Ktheory Together with Relative Generalizations, Interpretation in Terms of Grouprings.
Author(s): Aderemi Kuku, University of Iowa
141 Pages